A copolymer of a diallylamine and sulfur dioxide can be produced at high yields by copolymerizing a diallylamine and sulfur dioxide in the presence of a radical polymerization initiator in a polar solvent (for example, see Patent Document 1 or 2). A copolymer of a diallylamine and sulfur dioxide obtained by the above production process is water-soluble, and its use in a variety of fields such as a water-soluble coating composition and an agent for improving the dye fastness of a dyed article is proposed (for example, see Patent Document 1).